Papers by Keyword: Large Deformation

Abstract: The geometric nonlinearity resulting from large deformation of compliant members has continued to be an interesting research topic in nonlinear mechanics. In this study, two standard variational iteration algorithms, VIM-I and VIM-III are employed to investigate the large deformation of the continuum compliant beam under point load. The VIM is an efficient technique that bypasses the linearization process and proffers solutions to nonlinear problems. The horizontal and vertical displacements of the continuum compliant cantilever beam free end are expressed in explicit analytical forms. Numerical experiment and simulations were carried out to validate the efficacy and applicability of the semi-analytical method. The VIM-I was split into two; VIM-I(A) and VIM-I(B), with the difference being the initial approximations. The results from the VIM-I(A), VIM-I(B) and VIM-III algorithms were compared with the experimental and exact solution. The outcomes reveal that both algorithms correlated well with the analytical solution and experimental result.

Abstract: A constant strain hardening rate is characteristic for large strain deformation at low temperatures and often observed during wire drawing. This stage of deformation, in the following referred to as stage IV, is determined by the microstructural evolution of dislocation cells. At elevated temperatures, rapid stress saturation is typically reached and no stage IV behavior is observed. This behavior is modelled in the present work, following the concept of state-parameter based plasticity, evolving dislocation density and subgrain formation as functions of strain rate, strain and temperature. It is demonstrated that the temperature dependence of state parameters at different deformation stages is closely related. The present model is compared to a series of compression tests carried out on a Gleeble 1500 thermo-mechanical simulator. EBSD micrographs of the same material reveal the microstructural evolution during plastic deformation. It is shown experimentally that the transition from cell forming behavior to subgrain formation correlates well with the disappearance of stage IV and the overall change in the dominant mechanism for overcoming obstacles. In combination with thermally activated yield stress prediction, this model, recently implemented in the software package MatCalc, offers a powerful tool for flow-curve simulation.

Abstract: This work studies the large deformation behaviors of a re-entrant honeycomb subjected to the quasi-static tensile loading by employing the finite element (FE) package ABAQUS 6.11-2. The size effect of FE models is firstly investigated. Then, the deformation mechanism and stress-strain curve of a re-entrant honeycomb are discussed. Finally, the plastic Poisson’s ratio is calculated from the true strain and presented.

Abstract: The material point method is a particle-based method that uses a double Lagrangian-Eulerian discretisation. This approach has proved its functionality for the simulation of large deformation problems. Such problems are frequent in geotechnical engineering, more specifically those related to penetration during pile driving and conventional in situ tests such as the Cone Penetration Test. The shallow laboratory fall cone test is considered in this paper. This test is widely used for the determination of the liquid limit of clays, but it is also used to study the relationship between penetration (h) and the undrained shear strength of clays (s_u). Simulations are verified against laboratory vane shear tests and fall cone tests performed on samples of kaolin clay at different moisture contents. Calibrations using a simple penetration-strength (h-s_u) model are made based on a single coefficient named the cone factor (K). The numerical results closely match both the experimental data and analytical solutions available in the literature.

Abstract: Traditional grid-based numerical techniques such as the Finite Element Method (FEM) are known to suffer when large deformations of the continuum are encountered. As such, there has been limited success using this class of methods to solve many of the complex problems encountered in computational geomechanics. The potential of Meshfree techniques for addressing this perceived deficiency has been recognised. This study presents a robust Maximum Entropy Meshless (MEM) method for the analysis of problems involving geometrical nonlinearity in computational geomechanics. The method is validated via simulation of an undrained layer of soil under a rigid and rough strip footing undergoing large deformations and its merit is demonstrated through a comparison of the results with those obtained via the FEM.

Abstract: In computational contact mechanics, the contact constraints are usually applied using the Lagrange multiplier method, the penalty method, or alternative variants. Traditional contact approaches discretise the contact constraints in a weak sense, providing a stable interpolation scheme. However, they demand complicated search algorithms for contact detection at the interface between the intersecting bodies, and they usually lead to formulations that yield highly nonlinear tangent matrices, particularly for cases with realistic soil models and frictional contact. Recently, a new contact method based on the concept of a third medium has been developed, which overcomes the drawbacks of the conventional contact mechanics techniques. This new scheme is based on a space filling mesh in which the contacting bodies can move and interact. Contact constraints are enforced by changing the mechanical properties of medium with respect to the movements of the bodies. This new method has been developed for contact bodies undergoing large deformations using a hyper-elastic material law. In this study, the method is further extended to solve geomechanics problems in which the material behaviour is elastoplastic and the soil is subjected to large deformations. Potential merits of the third medium contact concept for analysing the geotechnical problems by the finite element method will also be addressed.

Abstract: In this work, 2-D/3-D forming problems (extrusion and deep drawing) are numerically simulated by extended finite element method (XFEM). The updated Lagrangian formulation is used to model the large deformation. The von-Mises yield criterion is used to model the elasto-plastic behavior assuming isotropic hardening. Penalty approach is employed to impose the contact constraints and non–penetration condition at the material interfaces. The level set approach is used for locating the material interfaces. The numerical simulations of two forming problems are presented using developed nonlinear XFEM code.

Abstract: Dielectric elastomer (DE) is gaining importance for potential strategic and commercial application as actuators. This paper reports the experimental investigation on different mechanical phenomena at large deformation of a commercially available acrylic dielectric elastomer material, VHB 4910 (3M) which is widely used for dielectric elastomer actuator (DEA) research. Attempts are made for accurate and precise experimental determination of nonlinear stress-strain, strain rate dependent hysteresis behaviour and cyclic softening of this material. It is observed that with the increase in strain rate maximum stress at a particular strain increases whereas hysteresis loss decreases. In the cyclic loading case after a particular number of cycles almost the hysteresis loss and maximum stress becomes constant. These experimental results are likely to be interesting for the designers for proper designing and characterization of the actuators fabricated with this material.

Abstract: In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10^-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

Abstract: In the past few years, owing to the vital role in maritime safety monitoring and marine hazard warning, stratospheric airship has become a research hotspot around the world. The structure of stratospheric airship is a typical aerated flexible membrane one. It is geometrical nonlinear in essence and it bears a distinct mechanical nature of large deformation. Therefore it makes optimizing the structure more difficult. The current studies of air-supported flexible membrane structural optimization ignore the uncertainty influence which is resulted from the loading environments, material properties and structural parameters. According to the Lagrangian Coordinate method, the deformed configuration is used as a reference in order to build accurate strain/displacement geometry. The Equilibrium equation is created by using the principle of virtual work. Meanwhile, the accuracy and stability of the solution is ensured by using the Updated Lagrangian Formulation. The uncertain parameters which are introduced during the analysis and optimization of the aerated flexible membrane structure are portrayed by interval mathematical theory. With respect to engineering application, the factors of uncertainty are considered. Maximizing the structural fundamental frequency (or first-order natural frequency) is taken as the objective, while structural integrity is taken as the constraint. Then the dynamic optimization is carried out under interval uncertainty. In this way the reliability of the membrane structure in complex conditions is improved and the probability of failure is reduced.